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Hilbert–Schmidt composition–differentiation operators on the unit ball

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Abstract

We use the notion of radial differential operator of order \(t>0\) to introduce the weighted composition–differentiation operator \(E^t_{\psi ,\varphi }(f)=\psi \cdot (R^t f)\circ \varphi \) on the Hardy and Bergman spaces of the unit ball and the polydisk in \(\mathbb {C}^n\). We obtain necessary and sufficient conditions on the functions \(\varphi \) and \(\psi \) to ensure that the operator \(E^t_{\psi ,\varphi }\) is Hilbert–Schmidt.

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  1. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149, Iran

    Ali Abkar

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  1. Ali Abkar
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Abkar, A. Hilbert–Schmidt composition–differentiation operators on the unit ball. Anal.Math.Phys. 14, 7 (2024). https://doi.org/10.1007/s13324-023-00865-z

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  • DOI: https://doi.org/10.1007/s13324-023-00865-z

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